Solve for $x$ : $ 5|x + 4| + 8 = 2|x + 4| + 5 $
Explanation: Subtract $ {2|x + 4|} $ from both sides: $ \begin{eqnarray} 5|x + 4| + 8 &=& 2|x + 4| + 5 \\ \\ { - 2|x + 4|} && { - 2|x + 4|} \\ \\ 3|x + 4| + 8 &=& 5 \end{eqnarray} $ Subtract ${8}$ from both sides: $ \begin{eqnarray} 3|x + 4| + 8 &=& 5 \\ \\ { - 8} &=& { - 8} \\ \\ 3|x + 4| &=& -3 \end{eqnarray} $ Divide both sides by ${3}$ $ \dfrac{3|x + 4|} {{3}} = \dfrac{-3} {{3}} $ Simplify: $ |x + 4| = -1$ The absolute value cannot be negative. Therefore, there is no solution.